Group 8 Main

Set work directories

set.seed(2020)
# setwd("~/Project3-FacialEmotionRecognition/doc")
# here replace it with your own path or manually set it in RStudio to where this rmd file is located. 
# use relative path for reproducibility

Provide directories for training data. Training images and Training fiducial points will be in different subfolders.

train_dir <- "../data/train_set/" # This will be modified for different data sets.
train_image_dir <- paste(train_dir, "images/", sep="")
train_pt_dir <- paste(train_dir,  "points/", sep="")
train_label_path <- paste(train_dir, "label.csv", sep="") 

Set up controls for evaluation experiments.

In this chunk, we have a set of controls for the evaluation experiments.

• (T/F) sample reweighting in model training

• (number) K, the number of CV folds

• (T/F) process features for training set

• (T/F) process features for testing set

• (T/F) Train PCA and create training and testing dataframes.

• (T/F) cross-validation on the GBM training set

• (T/F) GBM evaluation on an independent test set

• (T/F) cross-validation on the Random Forest (RF) training set

• (T/F) run evaluation on entire train set RF

• (T/F) run evaluation on an independent test set

• (T/F) reweighting the samples for training set

• (number) K, the number of CV folds

• (T/F) run evaluation on an independent test set

• (T/F) process features for test set

sample.reweight <- TRUE # run sample reweighting in model training
K <- 5  # number of CV folds

run.feature.train <- FALSE # process features for training set
run.feature.test <- FALSE # process features for test set
train.pca <- FALSE #Train and create training and testing PCA databases

run.cv_gbm <- FALSE # run GBM cross-validation on the training set
run.test_gbm <- TRUE # run GBM evaluation on an independent test set

run.cv.rf <- FALSE # run cross-validation on the training set for random forest 
run.train.rf <- FALSE # run evaluation on entire train set RF
run.test.rf <- TRUE # run evaluation on an independent test set

Using cross-validation or independent test set evaluation, we compare the performance of models with different specifications. In this part, we tune parameter n.trees and shrinkage for GBM.

# GBM parameters
n.trees <- c(500, 100, 1500)
shrinkage <- c(0.01, 0.05, 0.1)

Subsequently, I identify the following hyperparameters to tune the random forest model.

hyper_grid_rf <- expand.grid(
  ntree = c(200, 500, 800, 1000),
  mtry = c(20,50))

Import data and set up train-test split

#train-test split
info <- read.csv(train_label_path)
n <- nrow(info)
n_train <- round(n*(4/5), 0)
train_idx <- sample(info$Index, n_train, replace = F)
test_idx <- setdiff(info$Index, train_idx)
n_files <- length(list.files(train_image_dir))

Fiducial points are stored in matlab format. In this step, we read them and store them in a list.

#function to read fiducial points
  #input: index
  #output: matrix of fiducial points corresponding to the index

readMat.matrix <- function(index){
     return(round(readMat(paste0(train_pt_dir, sprintf("%04d", index), ".mat"))[[1]],0))
}

#load fiducial points
fiducial_pt_list <- lapply(1:n_files, readMat.matrix)
save(fiducial_pt_list, file="../output/fiducial_pt_list.RData")

Construct features and responses

• The follow plots show how pairwise distance between fiducial points can work as feature for facial emotion recognition.

  • In the first column, 78 fiducials points of each emotion are marked in order.
  • In the second column distributions of vertical distance between right pupil(1) and right brow peak(21) are shown in histograms. For example, the distance of an angry face tends to be shorter than that of a surprised face.
  • The third column is the distributions of vertical distances between right mouth corner(50) and the midpoint of the upper lip(52). For example, the distance of an happy face tends to be shorter than that of a sad face.

Figure1

feature.R house a feature engineering functions used to create the the GBM model.

• feature.R
• Input: list of images or fiducial point
• Output: an RData file that contains extracted features and corresponding responses

source("../lib/feature.R")
tm_feature_train <- NA
if(run.feature.train){
  tm_feature_train <- system.time(dat_train <- feature(fiducial_pt_list, train_idx))
  save(dat_train, file="../output/feature_train.RData")
}else{
  load(file="../output/feature_train.RData")
}
tm_feature_test <- NA
if(run.feature.test){
  tm_feature_test <- system.time(dat_test <- feature(fiducial_pt_list, test_idx))
  save(dat_test, file="../output/feature_test.RData")
}else{
  load(file="../output/feature_test.RData")
}

featur_pca.R houses a function used to create a PCA model. We will train a PCA model with the training set to use with RF, then apply the same PCA model to the testing set.

# create PCA features from Yiwen's function
source("../lib/feature_pca.R")
if(train.pca){
  
# train a PCA model
tm_pca_feature <- system.time({model_pca <- feature_pca(dat_train)})
# train both the training and test sets
feature_pca_train <- predict(model_pca, dat_train[, -6007])
feature_pca_test <- predict(model_pca, dat_test[, -6007])
save(feature_pca_train, file="../output/feature_pca_train.RData")
save(feature_pca_test, file="../output/feature_pca_test.RData")

}else{
load(feature_pca_train, file="../output/feature_pca_train.RData")
load(feature_pca_test, file="../output/feature_pca_test.RData")
}

The Baseline GBM Model

Train the GBM model with training features and responses

Call the train model and test model from library.

train.R and test.R should be wrappers for all your model training steps and your classification/prediction steps.

• train.R
  • Input: a data frame containing features and labels and a parameter list.
  • Output:a trained model
• test.R
  • Input: the fitted classification model using training data and processed features from testing images
  • Input: an R object that contains a trained classifier.
  • Output: training model specification
• In this part, we use GBM (baseline model) to do classification.

source("../lib/train_gbm.R") 
source("../lib/test_gbm.R")

Model selection with cross-validation

• Do model selection by choosing among different values of training model parameters.

source("../lib/cross_validation_gbm.R")
feature_train = as.matrix(dat_train[, -6007])
label_train = as.integer(dat_train$label)

if(run.cv_gbm){
  res_cv_gbm <- matrix(0, nrow = length(n.trees) * length(shrinkage), ncol = 6)
  count = 0
  for(i in 1:length(n.trees)){
    for(j in 1:length(shrinkage)){
      count = count + 1
      cat("n.trees =", n.trees[i], "\n")
      cat("shrinkage =", shrinkage[j], "\n")
      
      res_cv <- cv.function_gbm(features = feature_train, labels = label_train, K,
                              n.trees[i], shrinkage[j], reweight = sample.reweight)
      
      res_cv_gbm[count,] <- c(n.trees[i], shrinkage[j], res_cv[1], res_cv[2], res_cv[3], res_cv[4])
    }
  }
  
  colnames(res_cv_gbm) <- c("n.trees","shrinkage","mean_error", "sd_error", "mean_AUC", "sd_AUC")
  save(res_cv_gbm, file="../output/res_cv_gbm.RData")
}else{
  load("../output/res_cv_gbm.RData")
}

Visualize cross-validation results.

res_cv_gbm <- as.data.frame(res_cv_gbm) 
if(run.cv_gbm){
  p1 <- res_cv_gbm %>% 
    ggplot(aes(x = n.trees, y = mean_error,
               ymin = mean_error - sd_error, ymax = mean_error + sd_error)) + 
    geom_crossbar() +
    facet_wrap(~shrinkage)+
    theme(axis.text.x = element_text(angle = 90, hjust = 1))
  
  p2 <- res_cv_gbm %>% 
    ggplot(aes(x = n.trees, y = mean_AUC,
               ymin = mean_AUC - sd_AUC, ymax = mean_AUC + sd_AUC)) + 
    geom_crossbar() +
    facet_wrap(~shrinkage)+
    theme(axis.text.x = element_text(angle = 90, hjust = 1))
  
  print(p1)
  print(p2)
}

• Choose the “best” parameter value ADD A JUSTIFICAION HERE

# par_n.trees_best <- as.numeric(res_cv_gbm[which.min(res_cv_gbm$mean_error), 1])
# par_shrinkage_best <- as.numeric(res_cv_gbm[which.min(res_cv_gbm$mean_error), 2])
par_n.trees_best <- 500
par_shrinkage_best <- 0.05

• Train the model with the entire training set using the selected model (model parameter) via cross-validation.

# training weights
weight_train <- rep(NA, length(label_train))
for (v in unique(label_train)){
  weight_train[label_train == v] = 0.5 * length(label_train) / length(label_train[label_train == v])
}
tm_train <- NA
if (sample.reweight){
  tm_train <- system.time(fit_train <- train_gbm(feature_train, label_train, w = weight_train, par_n.trees_best, par_shrinkage_best))
} else {
  tm_train <- system.time(fit_train <- train_gbm(feature_train, label_train, w = NULL, par_n.trees_best, par_shrinkage_best))
}
save(fit_train, file="../output/fit_train_gbm.RData")

Run test on test images

tm_test = NA
feature_test <- as.matrix(dat_test[, -6007])
if(run.test_gbm){
  load(file="../output/fit_train_gbm.RData")
  tm_test <- system.time({prob_pred <- test_gbm(fit_train, feature_test, par_n.trees_best, pred.type = 'response');})
}

• evaluation

## reweight the test data to represent a balanced label distribution
label_test <- as.integer(dat_test$label)

weight_test <- rep(NA, length(label_test))
for (v in unique(label_test)){
  weight_test[label_test == v] = 0.5 * length(label_test) / length(label_test[label_test == v])
}
label_pred <- ifelse(prob_pred > 0.5, 1, 0)
label_test <- ifelse(label_test == 2, 1, 0)
accu <- sum(weight_test * (label_pred == label_test)) / sum(weight_test)
tpr.fpr <- WeightedROC(prob_pred, label_test, weight_test)
auc <- WeightedAUC(tpr.fpr)
cat("The accuracy of model:", "GBM with n.trees =" , par_n.trees_best, "and shrinkage =", par_shrinkage_best, "is", accu*100, "%.\n")
cat("The AUC of model:", "GBM with n.trees =" , par_n.trees_best, "and shrinkage =", par_shrinkage_best, "is", auc, ".\n")

Summarize Running Time

Prediction performance matters, so does the running times for constructing features and for training the model, especially when the computation resource is limited.

cat("Time for constructing training features=", tm_feature_train[3], "s \n")
cat("Time for constructing testing features=", tm_feature_test[3], "s \n")
cat("Time for training model=", tm_train[3], "s \n") 
cat("Time for testing model=", tm_test[3], "s \n")

Random Forest

Train a Random Forest model with training features and responses

Call the train_rf model and test_rf model from library.

Model selection with cross-validation

• Do model selection by choosing among different values of training model parameters.

We will Cross-validate hyperparameter “ntrees” and “mtry” with 5-fold validation to identify the combination that gives the highest AUC and lowest error.

• ntree: the default value for ntree is 500, so I’m choosing numbers below and above the default to test for results. The chosen ntree is: 200, 500, 800, 1000.

• mtry: the default value for mtry is 500, however, from experience, the smaller mtry will generate better results. Therefore, I pick 20 and 50 for tuning

# split features and labels
feature_train = as.matrix(feature_pca_train)
label_train = dat_train$label
# run cross-validation
if(run.cv.rf){
  res_cv_rf_pca <- matrix(0, nrow = nrow(hyper_grid_rf), ncol = 4)
  for (i in 1:nrow(hyper_grid_rf)){
    print(hyper_grid_rf$ntree[i])
    print(hyper_grid_rf$mtry[i])
    
    res_cv_rf_pca[i,] <- cv.function_rf(features = feature_train, 
                             labels = label_train, 
                             K,
                             ntree = hyper_grid_rf$ntree[i],
                             mtry = hyper_grid_rf$mtry[i])
  }
  save(res_cv_rf_pca, file="../output/res_cv_rf_pca.RData")
}else{
  load("../output/res_cv_rf_pca.RData")
}

• Visualize cross-validation results.

• Choose the “best” parameter value

tree_best_pca <- hyper_grid_rf$ntree[which.max(res_cv_rf_pca$mean_AUC)]
mtry_best_pca <- hyper_grid_rf$mtry[which.max(res_cv_rf_pca$mean_AUC)]

• Train the model with the entire training set using the selected model (model parameter) via cross-validation.

if (run.train.rf) {
  tm_train_rf_pca <- system.time(fit_train_rf_pca <- train_rf(feature_train, label_train, ntree = tree_best_pca, mtry = mtry_best_pca))
save(fit_train_rf_pca, tm_train_rf_pca, file="../output/fit_train_rf_pca.RData")
} else {
  load(file="../output/fit_train_rf_pca.RData")
}

Run test on test images

tm_test_rf_pca = NA
feature_test <- as.matrix(feature_pca_test)
label_test <- dat_test$label
if(run.test.rf){
  load(file="../output/fit_train_rf_pca.RData")
  tm_test_rf_pca <- system.time(label_pred <- as.integer(predict(fit_train_rf_pca, feature_test)))
}

Evaluation

Summarize Running Time

Prediction performance matters, so does the running times for constructing features and for training the model, especially when the computation resource is limited.

Reference

• Du, S., Tao, Y., & Martinez, A. M. (2014). Compound facial expressions of emotion. Proceedings of the National Academy of Sciences, 111(15), E1454-E1462.